One of the goals of my research is to understand the emergent behaviour in continuum and multi-particle systems with non-local interactions. The models I have worked on have demonstrated emergence of very complex behaviour as a consequence of individuals following simple interaction rules, without any leader or external coordination. Indeed, natural swarms (birds or fish for instance) achieve self-organizing behaviour through local signalling, in the absence of a centralized decision-making mechanism. Such biologically-inspired swarming considerations are at the core of the models I have studied.
From the point of view of theory, I have investigated qualitative properties of swarm equilibria (in free space, as well as in domains with boundaries), existence of global minimizers of the interaction energy, regularization by diffusion, the effect of anisotropy, and extensions of aggregation models to surface and manifold settings. In terms of applications, I have worked on biological swarms, autonomous robots, opinion formation and crime modelling. Click on the link below to find my publications.
Math Links